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## Warm-Up

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### Warm-Up What does the motion of gas molecules look like? Why does a balloon inflate when you blow it up? Why will soda explode from a bottle if opened after shaking it? – PowerPoint PPT presentation

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Title: Warm-Up

1
Warm-Up
• What does the motion of gas molecules look like?
• Why does a balloon inflate when you blow it up?
Why will soda explode from a bottle if opened
after shaking it?

2
Chapter 5
• The Gas Laws

3
Section 5.1- Pressure
• Force per unit area (P force/area).
• Gas molecules fill container.
• Molecules move around and hit sides.
• Collisions are the force.
• Container is the area.
• Measured with a barometer.

4
How Does A Barometer Work?
Vacuum
760 mm Hg
• The pressure of the atmosphere at sea level will
cause the column of mercury to rise to 760 mm Hg.
• 1 atm 760 mm Hg

Pressure of atmosphere pushes on Hg
As a result, Hg rises up into the glass tube
Hg stops rising when its equal to atmospheric
pressure
5
Units of pressure
• 1 atmosphere 760 mm Hg
• 1 mm Hg 1 torr
• 1 atm 101,325 Pascals 101.325 kPa
• The first two are provided on the AP equation
sheet. No need to memorize the third- I assume
youll be given that if you need to use it.

6
THE GAS LAWS OF BOYLE, CHARLES, AND AVOGADRO
• Section 5.2

7
• You should be aware of the following laws,
however we will not focus heavily on them as they
can be derived from the ideal gas law.
• After briefly going through each of the following
laws, we will see how to derive each from the
ideal gas law.

8
Boyles Law
• Pressure and volume are inversely related at
constant temperature.
• P1V1 P2V2
• As one goes up, the other goes down.
• Ex if P increases (at constant T), V must go
down
• Further studies show that Boyles Law is only
true at very low P
• This will be discussed more in 5.8
• Gases that obey these laws are called ideal
gases.

9
Charless Law
• Volume of a gas varies directly with the
temperature at constant pressure.
• V1 V2
• T1 T2
• As one goes up/down, so does the other.

10
• At constant temperature and pressure, the volume
of gas is directly related to the number of
moles.
• V1 V2
• n1 n2
• As one goes up/down, so does the other.

11
Gay- Lussac Law
• At constant volume, pressure and temperature are
directly related.
• P1 P2
• T1 T2
• As one goes up/down, so does the other.

12
Combined Gas Law
• Combination of Boyles Law, Charles Law, and
Gay-Lussac Law.
• Moles of gas remain constant.
• P1V1 P2V2
• T1 T2

13
Summary
• Boyles P1V1 P2V2
• Charles V1/T1 V2/T2
• Avogadros V1/n1 V2/n2
• Gay-Lussac P1/T1 P2/T2
• Combined P1V1/T1 P2V2/T2
• Thats a lot of laws! Or we can just use the
Ideal Gas Law!

14
Combined Gas Law Cont.
• Ex A 2.3L sample of gas has a pressure of 1.2atm
at 200.K. If the pressure is raised to 1.4atm and
the temperature is increased to 300.K, what is
the volume of the gas?
• V2 P1V1T2
• T1P2
• V2 3.0 L

15
Practice
• Ex A 12.2L sample of gas has 0.50mol of O2 at
1atm and 25C. How many moles of O2 would occupy
19.4L at the same temperature and pressure?
• Solution V1/n1 V2/n2
• (12.2L)/(0.50mol) (19.4L)/(n2)
• n2 0.80mol
• In other words, 0.80mol of O2 would be required
to fill 19.4L in order to keep the same pressure
as 0.50mol of O2 in 12.2L.

16
AP Practice Question
• A sample of argon gas is sealed in a container.
The volume of the container is doubled. If the
pressure remains constant, what must happen to
the temperature?
• It doesnt change.
• It is halved.
• It is doubled.
• It is squared.

17
Demonstration Warm-Up!
• Observe the demonstration.
• Keep in mind the properties of gases we have
discussed so far P, V, T, and n.
• Think about these properties before and after
imploding the can. Why do you think the can was
crushed?
• As temperature decreases, so does the pressure
and volume.
• Remind you of a law we looked at?

18
Sections 12 Homework
• Pgs. 217-218 2, 6, 34, 35

19
THE IDEAL GAS LAW
• Section 5.3

20
Ideal Gas Law
• PV nRT
• At standard temperature and pressure (STP) V
22.4L at 1atm, 0ºC, and n 1mol. These
conditions were used to determine R (ideal gas
constant)
• R 0.08206 L atm/mol K
• 8.314 J/mol K
• 62.36 L torr/mol K
• Tells you about a gas NOW.
• The other laws tell you about a gas when it
changes.

KNOW THIS!
Choose R value according to units of P
21
Ideal Gas Law Cont.
• Looking back at the possible values for R, you
will notice that all units for temperature are in
K.
• When using the ideal gas law for calculations,
convert all temperatures to K!
• Recall conversion K C 273 (provided on AP
equation sheet)

22
Ideal Gas Law Derivation Practice
• May be asked to prove one of the laws discussed
before!
• Strategy get all constants in the ideal gas law
on one side and changing variables on the other.
• We will go several of these in class.

23
AP Practice Question
• A 1.15mol sample of carbon monoxide gas has a
temperature of 27C and a pressure of 0.300atm.
If the temperature is lowered to 17C at constant
volume, what is the new pressure?
• a) 0.290atm c) 0.206atm
• b) 0.519atm d) 0.338atm

24
Ideal Gas Law- Why Ideal?
• Ideal gases are hypothetical substances.
• Gases only approach ideal behavior at low
pressure (lt 1 atm) and high temperature.
• They do not behave exactly according to this law,
but they behave closely enough.
• Law provides good estimates of gas behavior under
these conditions.
• Unless told otherwise, assume ideal gas behavior
and use the ideal gas law.

25
AP Practice Question
• A sample of aluminum metal is added to HCl. How
many grams of aluminum metal must be added to an
excess of HCl to produce 33.6L of hydrogen gas at
STP?
• 18.0g
• 35.0g
• 27.0g
• 4.50g

26
Section 3 Homework
• Complete the gas laws worksheet AND 33, 40, 43,
52 on pg. 219-221.

27
GAS STOICHIOMETRY
• Section 5.4

28
Gases and Stoichiometry
• Reactions involve moles of substances.
• Recall that at STP (0ºC and 1 atm) 1mol of any
gas occupies 22.4 L.
• At STP this can be a conversion factor
1mol/22.4L or 22.4L/1mol
• If not at STP, use the ideal gas law to calculate
moles or volume of a substance.

29
Section 4 Example
• Quicklime (CaO) is produced by the thermal
decomposition of calcium carbonate. Calculate the
volume of carbon dioxide produced at STP if 152g
of calcium carbonate are completely decomposed.
• CaCO3 ? CaO CO2
• Convert to moles 152g x 1mol 1.52mol

• 100.09g CaCO3
• 11 mole ratio of CaCO3 to CO2 1.52mol CO2
• Use STP conditions stoichiometry
• At STP 1mol 22.4L
• 1.52mol x (22.4L/1mol) 34.1L CO2

Can double check using ideal gas law
30
Gas Density and Molar Mass
• Recall D m/V
• Let mmolar stand for molar mass
• mmolar m/n so n m/mmolar
• PV nRT solve for n n PV/RT
• Thus m/mmolar PV/RT
• Solve for mmolar mmolar mRT/VP
• Replace m/V with D mmolar DRT/P
• If density, temperature, and pressure are known,
molar mass can be found.

31
AP Practice Question
• Determine the formula for a gaseous silane
(SinH2n2) if its density is 5.47g/L at 0ºC and
1.00atm.
• There are several ways to solve!
• SiH4
• Si2H6
• Si3H8
• Si4H10

32
Section 4 Homework
• Pg. 220-221 51, 54, 57, 63, 64

33
DALTONS LAW OF PARTIAL PRESSURES
• Section 5.5

34
Daltons Law of Partial Pressures
• The total pressure in a container is the sum of
the pressure each gas would exert if it were
alone in the container.
• Total pressure sum of partial pressures.
• Ptot P1 P2 P3 ...
• P1, P2, P3 are individual gases
• From the ideal gas law PTotal (nTotal)RT

V
35
Partial Pressures Cont.
• What does Daltons Law tell us about ideal gases?
• Total of gas particles, not their identities,
is important.
• V of individual gas particles doesnt affect the
total P.
• Forces between gas particles doesnt affect the
total P.
• If these were important, the different identities
of gas particles would affect the total P
differently.

36
AP Practice Question
• A gaseous mixture at 25C contained 1mol CH4 and
2mol O2, and P 2atm. The gases underwent the
following reaction
• CH4(g) 2O2(g) ? CO2(g) 2H2O(g)
• What is the P in the container after the reaction
goes to completion and the T is allowed to return
to 25C?
• 1atm
• 2atm
• 3atm
• 4atm

37
AP Practice Question
• A sealed, rigid container is filled with three
identical gases A, B, and C. The partial
pressure of each gas is known as well as T and V.
What additional information is needed to find the
masses of the gases in the container?
• a) average distance travelled between molecular
collisions
• b) the intermolecular forces
• c) the molar masses of the gases
• d) the total pressure

38
The mole fraction
• Ratio of moles of a substance to the total moles.
• symbol is Greek letter chi c
• c1 n1 P1
• ntot Ptot
• Mole fractions have no units!

39
AP Practice Question
• A reaction makes a mixture of CO2, CO, and H2O.
The gaseous products contained 0.60mol CO2,
0.30mol CO, and 0.10mol H2O. If the total P is
0.80atm, what is the partial P of CO?
• 0.24atm
• 0.34atm
• 0.080atm
• 0.13atm

40
Vapor Pressure
• Water evaporates!
• When water evaporates, the resulting water vapor
has a pressure.
• Vapor pressure changes with T- must be looked up.
• Gases are often collected over water so the vapor
pressure of water must be subtracted from the
total pressure.
• Vapor pressure must be given.

41
AP Practice Question
• A sample of methane gas was collected over water
at 35C. The sample had a total pressure of 756mm
Hg. Determine the partial pressure of methane gas
in the sample. (Vapor pressure of water at 35C
is 41mm Hg.)
• 760mm Hg
• 41mm Hg
• 715mm Hg
• 797mm Hg

42
Section 5 Homework
• Pg. 221-222 65, 67, 69, 72

43
Collapsing Can Demo
• Watch the demonstration.
• Why did the can collapse?
• -The heat vaporized the water, which in turn
increased P and pushed air out of the can.
• -When the can was inverted the water vapor
quickly cooled. This caused a quick drop in P
(created a partial vacuum because essentially no
air was left to maintain P).
• -The atmospheric P outside of the can was much
greater than P inside of the can, which allowed
the can to be crushed.

44
THE KINETIC MOLECULAR THEORY OF GASES
• Section 5.6

45
Kinetic Molecular Theory (KMT)- Explains Behavior
Properties of Gases
• Gases are made up of molecules or atoms.
• V of particles can be ignored (very small in
comparison to distance b/t particles).
• Particles constantly move and collide with each
other and the walls of the container. Collisions
with the walls of the container cause P of the
gas.
• Particles dont attract or repel each other when
they collide, its elastic (no KE is lost- its
transferred).
• The average KE is proportional to the Kelvin T.

46
KMT Cont.
• Assumes gases are ideal.
• BUT no gases are truly ideal- they only approach
ideal behavior (specifically nonpolar gases at
low P and high T).
• In reality, gases DO have V (although small), and
they CAN interact with each other.
• Even so, assuming ideal behavior gives us good

47
KMT
• 3 describes motion lets quantify it
• urms v(3RT/mmolar)
• urms is root mean square velocity
• R value used is 8.314J/molK
• molar mass in kg/mol (b/c J kgm2/s2)
• 5 KE per mole (average KE) 3/2 RT
• Recall definition of T! Directly related!
• Units J/mol
• KE per molecule ½ mv2 ? this is the only
equation given on AP exam!
• - Units J

Large! For H2 at 20C 2,000m/s
48
Root Mean Square Velocity Example
• What is the root mean square velocity for the
atoms in a sample of He gas at 25C?
• Convert T to K 25 273 298K
• M 4.00g/mol ? 0.004000kg/mol
• urms 136m/s

49
Range of velocities
• The average distance a molecule travels between
collisions with another gas particle is called
the mean free path and is small (near 10-7)
• Results in a range of velocities.
• Temperature is an average. There are molecules of
many speeds in the average.
• This is shown on a graph called a velocity
distribution.

50
Maxwell-Boltzmann Distribution
Notice that with higher T, average velocities
increase and so does the velocity range.
273 K
1273 K
2273 K
number of particles
Molecular Velocity
51
AP Practice Question
• Two balloons are at the same T and P. One
contains 14g of nitrogen and the other contains
20.0g of argon. Which of the following is true?
• D of N2 gt D of Ar
• Average speed of N2 gt average speed of Ar
molecules
• Average KE of N2 molecules gt average KE of Ar
molecules
• V of N2 container lt V Ar

52
AP Practice Question
• Increasing the T of an ideal gas from 50C to
75C at constant V will cause which of the
following to increase for the gas?
• average molecular mass of the gas
• average distance between molecules
• average speed of the molecules
• density of the gas

53
Section 6 Homework
• Pg. 222-223 78, 79, 82, 83

54
EFFUSION AND DIFFUSION
• Section 5.7

55
Effusion
• Passage of gas through a small hole, into a
vacuum.
• Effusion rate speed at which the gas is
transferred into the vacuum.
• Grahams Law - the relative rates of effusion are
inversely proportional to the square roots of the
molar masses of the gas particles.

56
Diffusion
• The spreading of a gas through a room (mixing of
gases).
• Slow considering molecules move at hundreds of
meters per second.
• Slower movement is caused by collisions with
other molecules in the air.
• Best estimate is Grahams Law.
• Ratio is actually less.
• More complex analysis required.

57
Section 7 Homework
• Pg. 223 86, 88

58
REAL GASES
• Sections 5.8 5.9

59
Real Gases
• Real molecules do take up space and they do
interact with each other (especially polar
molecules).
• Need to add correction factors to the ideal gas
law to account for these.
• a correction factor for pressure
• b correction factor for volume

60
Volume Correction
• The actual volume free to move in is less because
particles do take up some of the volume.
• More molecules will have more effect (taking up
more space).
• Corrected volume V V - nb
• b is a constant that differs for each gas.
• P nRT (V-nb)

61
Pressure Correction
• Molecules are attracted to each other- pressure
on the container will be less than ideal gases.
• Size of correction factor depends on the of
molecules per liter (conc. of gas).
• More molecules closer together and more likely
to interact/attract.
• Since two molecules interact, the effect must be
squared.

(
)
2
a proportionality constant
Pobserved
P - a
62
All Together
(
)
• Pobs nRT - a n 2 V-nb
V
• Called the Van der Waals equation if
rearranged
• Corrected Corrected Pressure
Volume

NOT given on AP Equation sheet!
63
Graphing Real Gases
• For ideal gases PV/nRT should be 1 (since both
are equal according to ideal gas law).
• Not seen for real gases.
• Notice the effect of T on ideal gas behavior.

64
Graphing Real Gases
• Deviation from ideal behavior depends on identity
of the gas too.
• Smaller, nonpolar gases exhibit more ideal
behavior.

65
Where Do Constants Come From?
• a and b are experimentally determined.
• Different for each gas.
• Bigger molecules have larger b.
• a depends on both size and polarity.
• Note table of constants for some gases is on pg.
210 in the book.

66
Graphing Real Gases
• Take a closer look at H2 on the graph.
• Most ideal behavior, so it has lowest a value
of the gases shown for Van der Waals equation.
• Lower a means less correction needed.
• Thus it must have weak intermolecular forces.
• Real gas behavior can tell us how big of a role
intermolecular forces play in attraction between
gas molecules.

67
AP Practice Question
• The true volume of a real gas is smaller than
that calculated from the ideal gas equation. This
occurs because the ideal gas equation does not
consider which of the following?
• Attraction between molecules
• Shapes of molecules
• Volume of molecules
• Mass of molecules

68
AP Practice Question
• Which of the following gases probably shows the
greatest deviation from ideal gas behavior?
• He
• O2
• SF4
• SiH4

69
Sections 89 Homework
• Pg. 223 89, 90